i.e. I want to remove all information, that was backed up from my phone to the Google servers (sync data, etc). How can I do that?
Go to Google Dashboard and sign in with the same Google account you used on your phone. Click the arrow next to Android to see a list of all your devices with backup data. At the bottom is a button, Delete backup data. This button deletes the backed-up data from all devices. There's no way to delete the data from a specific device.
If you want to delete not only the data backed up using the "Back up my data to Google servers" option, but also other synced data like Gmail, contacts, calendars, Google Docs documents, you'll find them listed in their own sections on the same dashboard page.
Delete Device History
To delete the stuff backed up under Settings -> Backup & reset like saved contacts, the list of installed apps, saved WiFi networks, etc. go to Device History and select and delete the backups you want to remove. Or you can use the three-dot menu in the upper-right corner to view more Delete options to delete all backups.
Delete Saved App Data
Some apps will save data to your Google Drive account. To remove these, go to Google Drive and click the settings gear icon in the upper-right. Select Settings and then Manage Apps. From there you can view the list of connected apps, including ones installed on your phone and disconnect them and/or delete any data stored by them.